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Angle sums: cheat sheet

Angles and shapes · The words and methods from the lessons, with an example of each.

interior angle

An angle inside a shape, at one of its corners.

∠A\angle A

regular polygon

All sides and all angles are equal, so each angle is the angle sum shared equally: a regular hexagon has angles of 120∘120^\circ.

each angle=(n−2)×180∘n\text{each angle} = \dfrac{(n - 2) \times 180^\circ}{n}

angle sum of a polygon

Split it into triangles from one corner: a shape with nn sides makes n−2n - 2 triangles. A pentagon: 3×180∘=540∘3 \times 180^\circ = 540^\circ.

(n−2)×180∘(n - 2) \times 180^\circ
A pentagon splits into 3 triangles from A: 540°
A pentagon splits into 3 triangles from A: 540°

polygon

A closed shape with straight sides: triangle (3), quadrilateral (4), pentagon (5), hexagon (6), octagon (8).

n sides,  n cornersn \text{ sides}, \; n \text{ corners}

angle sum of a triangle

True for every triangle, whatever its shape or size: tear off the corners and they fill a straight line.

a+b+c=180∘a + b + c = 180^\circ
An obtuse triangle: 24° + 127° + 29° = 180°
An obtuse triangle: 24° + 127° + 29° = 180°